Find z - transform F(z) of the function-1 f(nT) = d"" -T z - a T z + a | Z - O خيار 2 3 T z – a -T z + a 1 us

Q: 4. (a) Prove that H, { f(x) [Hn-1{f(x)} + Hn+1{f(x)}] and hence find T. 2n S (x – a) Hn ,a > 0, k >…

A:

Q: Determine the z-transform of the sequence x(n) = 3"u(n – 3) using z-transform properties. Express…

A:

Q: Determine the z-transform of the sequence (1 + n)u(n) using z-transform properties. Express X(z) as…

A:

Q: 5. Compute the inverse z-transform of X(z)=log(1+z),z|<1.

A: Given: To explain the given statement as follows, To calculate Z transform, .

Q: The inverse z-transform of (a) (-a)" [] 2₁] e-a-3 (z-ea)(z-3) -, a>0 ROC: ea <z<3 is,

A:

Q: Z-transform x(n) = a¹sin (w¸n) u(n)

A:

Q: : The Z-Transform of X(z) = n(u-3) is %3D

A: For a given real or complex sequence of discrete-time signals, the Z-transform converts this signal…

Q: Determine the Discrete-Time Fourier Transform and z-Transform of the signal given below.…

A:

Q: 16. The even function f(t) = -t + 1; – 1 <t < 0; f(t + 2) = f(t) has Fourier coefficients -2 ao = 3…

A:

Q: Find the z-transform of the following x[n]: x[n] = {{, 1, − }} x[n] = 28[n+ 2]- 38[n - 2] x[n] = 3(…

A: Introduction: The Z-transformation is the way to transform a discrete time signal into a complex…

Q: : Determine the z-transform of the following; 6. x(n) = n (n + 1) u(n)

A: To determine Z transformation of xn=nn+1un Now, xn can be re-written as xn=nn+1un=n2un+nun It is…

Q: The Z-Transform of X(z) =5 (2^n)(u-2) is 5z/(z-2) True False

A: We're going to solve

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

A:

Q: 6. Evaluate the inverse z-transform of x(z)= 2z-1 (1-2z-¹)²

A:

Q: Example 8: Find the Fourier transform of the function 1+ for - a <x <0 a f(x) = 1 1- for 0<x<a a 0,…

A:

Q: Find the sequence x(k) if the Z-Transform of the sequence is given as 22 + z (2-2) (z-1) F(z) x{k} =…

A:

Q: Determine the z-transform of the sequence x(n) = 3"u(n – 3) using z-transform properties. Express…

A:

Q: 4. Obtain the z-transform of the following: A. B. C. D. X(z) X(z) X(z): X(z) x(n) = I = n (⑥)", -12…

A: p

Q: The Fourier transform of f(t) = -1<t<1 is otherwise O 2sin(w + 2) w +2 O 2sin(w – 2) w - 2 2…

A: Fourier transform of the function

Q: The Z-transform of the following function f[k] = 2 + (-5)*-(-4)* is so the constants A and B…

A: What is Z-transformation: Z-transformation is a discrete transformation through which one can…

Q: 2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT DTFT 1 if…

A:

Q: (A) Compute the discrete Fourier transform of f = 2 – 2t on [–1,3) with length 4. F{f} = |

A: (A) Consider the given equation: Length N=4 Time division is 13 Then Then, Now, So,

Q: Find the inverse z-transform of z(-5z+22) / (z+1)(z-2)².

A:

Q: 1. Find the Fourier Sepise of 4x: 0<x< T f(x) {" 1:-π<x<0 on interval-A

A:

Q: The Z-transform of the following function f[k] =22*+/- (-5)*(-4)* is So the constants A and B…

A: z transform

Q: Obtain the z-transform of the following: x(n)=na" sin(an)u(n)

A: Let us start solving the problem step by step.... We need to find the z-transform of x(n)

Q: 4.21. Find the inverse z-transform of 2 2 -- 5z2 +z+3 X(z) = Iz|<1 (z-1)(2-2)

A: Solution

Q: Find the Inverse Z-transform for X(z)=(z+1)/((z-1)(z-2)(z-3))

A:

Q: 2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT (a) ifx[n]…

A: Given x[n]⇔DTFTXejω then we have to show x[n-n0]⇔DTFTXejωe-jn0ω=Z(ejω) (say) Proof: we have…

Q: The Z-Transform of x (n) = e-3(n-4) cos(0.17 (n-4))u (n- 4) Where u(n-4) = 1 for n 24 while u(n-4) =…

A: We have to find the Z transform

Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: Find the z - transform of IN k

A:

Q: Find the Z-transform for x(n) shown below * including ROC a(n) = (3)"sin(프n)u(n) |

A: It is given that, x(n)=13nsinπ4nu(n) The convolution property says that,   The z-transform of…

Q: If the Z- Transform of x(k) is X(z) = 7/ (z - 1) and x(0) = x(1) = 1 What's the Z- Transform of…

A:

Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

A:

Q: 3. Compute the inverse z-transform x[n] of the X(z) where X(z) = (z² + 2) {(z? + 1)(z – 1)}

A:

Q: 1. Consider the function [x-1, f(x) = 0, (1.1) Find the Fourier transform of f(x). if 0 ≤ x ≤ 1,…

A: For part 1.1, we are given the function f(x)=x-1,           if  0≤x≤10,                  elsewhere…

Q: 2. Compute the Fourier Transform of f(x) = e¬ax²

A:

Q: Laplace transform of (1 – e-Tt)2 is 2 2 1 s +7 2 s + 14 1 1 s+7 s+ 14 2 + s+7 3 1 1 14 1 1 s+7 s +…

A:

Q: The z-transform of x[n] (-0.7)-Fu[n-5] is X(2) =i %3D 1지> 0.7 %3D 1+0.7z1 O True O False

A:

Q: Compute the discrete Fourier transform of g = t + 1 on [0, 4) with length 3.

A: Given:                              gt=t+1, t∈[0,4) with length 3 To find: Discrete Fourier…

Q: Find the Fourier transform of f (x) defined by |x| a f (x) = sin? ax ta and hence prove that x2 2

A:

Q: Q1: Proof that the solution of inverse Z transform: z3 – z2 + 2z F(z) = (z + 1)(z – 1)² Is f(k) =…

A: Decompose the given z transform in partial fraction and get it in recognizable form:

Q: 4. Find the inverse z transform of [z(4z -8z +5)]/[(z+1)'(z - 2)]

A: Given The given z transform is Apply formula

Q: The Z-transform of the following function f[k] =22*+/-(-5)* – ²³ (-4)* is So the constants A and B…

A:

Q: The Z-transform of the following function f[k] =2k +(-5)* - (-4)* is so the constants A and B…

A:

Q: find the inverse z-transform * X(z) =- (z-1)(z +0.4z -0.32)

A: Given that, X(z)=z2(z-1)(z2+0.4z-0.32) This can be written as,…